(Cambridge Studies in Advanced Mathematics 146) Jan-Hendrik Evertse, Kalman Gyory - Unit Equations in Diophantine Number Theory-Cambridge University Press (2015)

CAMBRIDGE STUDIES IN ADVANCED MATHEMATICS 146
Editorial Board
B. BOLLOB ´ AS, W. FULTON, A. KATOK, F. KIRWAN,
P. SARNAK, B. SIMON, B. TOTARO
UNIT EQUATIONS IN
DIOPHANTINE NUMBER THEORY
Diophantine number theory is an active area that has seen tremendous growth over the
past century, and in this theory unit equations play a central role. This comprehensive
treatment is the first volume devoted to these equations. The authors gather together all
the most important results and look at many different aspects, including effective results
on unit equations over number fields, estimates on the number of solutions, analogues for
function fields, and effective results for unit equations over finitely generated domains.
They also present a variety of applications. Introductory chapters provide the necessary
background in algebraic number theory and function field theory, as well as an account
of the required tools from Diophantine approximation and transcendence theory. This
makes the book suitable for young researchers as well as for experts who are looking
for an up-to-date overview of the field.
Jan-Hendrik Evertse works at the Mathematical Institute of Leiden University. His
research concentrates on Diophantine approximation and applications to Diophantine
problems. In this area he has obtained some influential results, in particular on estimates
for the numbers of solutions of Diophantine equations and inequalities. He has written
more than 75 research papers and co-authored one book with Bas Edixhoven entitled
Diophantine Approximation and Abelian Varieties.
K´ alm´ an Gy˝ ory is Professor Emeritus at the University of Debrecen, a member of the
Hungarian Academy of Sciences and a well-known researcher in Diophantine number
theory. Over his career he has obtained several significant and pioneering results, among
others on unit equations, decomposable form equations, and their various applications.
His results have been published in one book and 160 research papers. Gy˝ oryisalsothe
founder and leader of the number theory research group in Debrecen, which consists of
his former students and their students.

CAMBRIDGE STUDIES IN ADVANCED MATHEMATICS
Editorial Board:
B. Bollob´ as, W. Fulton, A. Katok, F. Kirwan, P. Sarnak, B. Simon, B. Totaro
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Unit Equations in
Diophantine Number Theory
JAN-HENDRIK EVERTSE
Universiteit Leiden
K´ ALM ´ AN GY ˝ ORY
Debreceni Egyetem, Hungary

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